Apart from the world of trouble you might get yourself into when doing such things on secured systems, why are you going at it in such a complicated way?
Why not simply use a self hosted file/document storage and sharing solution like Nextcloud or Pydio Cells or something like that? Reachable through standard HTTP(S), which is a lot easier to reach than most other protocols.
As far as I understood from some research is that I would need to install and run an DHCP server on my laptop, which they did not recommend.
Or simply set up the Pi with a static IP.
there does not seem to be a standard for connecting to a device directly over a single cable and login with a user account.
There is. A cable. You just need two non-identical IPs from the same subnet, e.g. 10.0.0.1 and 10.0.0.2 or whichever you want from the private ranges.
Why would I need a separate router for that? I’d need to configure the main router anyway.